Real-time coordinated estimation of passenger demand of urban rail transit and network-wide passenger flow dynamics in a computational-graph framework

The real-time estimation of origin-destination (OD) matrices and passenger flow dynamics in urban rail transit is essential for efficient operations but is hindered by challenges such as data scarcity, high dimensionality, and spatiotemporal dynamics. This study proposes a feedback-enhanced iterative estimation framework that leverages multi-source data to achieve coordinated estimation<br/>of OD demand and link-level passenger flows. The framework incorporates a path-to-link temporal correlation matrix to model spatial-temporal dependencies and a time-extended, four-layer computational graph to address high-dimensional complexity. A temporal feedback mechanism embedded in the backward propagation process iteratively refines earlier estimates by calibrating them against errors observed in later intervals, enabling the framework to adapt to dynamic transit environments. Validation on the Sioux-Falls and Beijing metro networks demonstrates the framework’s scalability, robustness, and high accuracy, achieving an average estimation accuracy of 98.86%. The experimental results show its potential to enhance operational decision-making in urban rail transit systems.